Metallic wall hall thrusters

ABSTRACT

A Hall thruster apparatus having walls constructed from a conductive material, such as graphite, and having magnetic shielding of the walls from the ionized plasma has been demonstrated to operate with nearly the same efficiency as a conventional nonmagnetically shielded design using insulators as wall components. The new design is believed to provide the potential of higher power and uniform operation over the operating life of a thruster device.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 13/768,788 filed on Feb. 13, 2015, which, in turn claimspriority to and the benefit of U.S. provisional patent application Ser.No. 61/599,174, filed Feb. 15, 2012, and priority to and the benefit ofU.S. provisional patent application Ser. No. 61/745,041, filed Dec. 21,2012, each of which applications is incorporated herein by reference inits entirety.

STATEMENT REGARDING FEDERALLY FUNDED RESEARCH OR DEVELOPMENT

The invention described herein was made in the performance of work undera NASA contract, and is subject to the provisions of Public Law 96-517(35 USC 202) in which the Contractor has elected to retain title.

THE NAMES OF THE PARTIES TO A JOINT RESEARCH AGREEMENT

NOT APPLICABLE.

INCORPORATION-BY-REFERENCE OF MATERIAL SUBMITTED ON A COMPACT DISC

NOT APPLICABLE.

FIELD OF THE INVENTION

The invention relates to electric propulsion devices in general andparticularly to Hall thrust devices.

BACKGROUND OF THE INVENTION

Hall thrusters generate thrust through the formation of an azimuthalelectron current that interacts with an applied, quasi-radial magneticfield to produce an electromagnetic force on the plasma. These thrustersprovide an attractive combination of thrust and specific impulse for avariety of near-earth missions and, in many cases, they allow forsignificant reductions in propellant mass and overall system costcompared to conventional chemical propulsion. The range of thrust andspecific impulse attainable by Hall thrusters makes them applicable alsoto a variety of NASA science missions. Many such missions howeverrequire wider throttling and larger propellant throughput thannear-earth applications. A critical risk associated with the applicationof Hall thrusters to science missions is their throughput capability.There are two major wear processes known to exist in Hall thrusters thatcan limit their applicability to such missions: erosion of theacceleration channel and erosion of the hollow cathode.

Multiple approaches have been pursued to reduce or eliminate this risk.For example, the high voltage, Hall accelerator (HiVHAc) incorporates aninnovative discharge channel replacement technology as a means ofextending its life. In 2008 the NASA-103M.XL version of HiVHAcaccumulated more than 4,700 h at 700 V upon the completion of a weartest. More recently, a Qualification Life Test (QLT) of a different Hallthruster, the BPT-4000, was extended beyond 10,400 h. The BPT-4000 isnominally a 4.5-kW class thruster, and has fixed insulators and amagnetic design for high efficiency and long life. Post-test assessmentof the wear data showed no measurable erosion of the accelerationchannel walls from 5,600 h to 10,400 h indicating that the thrusterreached an approximately “steady state” erosion configuration. TheBPT-4000 QLT results were explained in a paper Mikellides, I. G., Katz,I., Hofer, R. R., and Goebel, D. M., de Grys, K., and Mathers, A.,“Magnetic Shielding of the Channel Walls in a Hall Plasma Accelerator,”Physics of Plasmas, Vol. 18, No. 3, 2011, p. 033501, which suggests thatif properly designed, the life of Hall thrusters can be extended to (orexceed) that of ion thrusters thereby retiring the risk associated withtheir throughput capability.

The BPT-4000 QLT has exceeded significantly the requirements for mostcommercial or military missions. However, because many NASA sciencemissions require longer operational times, higher throughput, and awider range of operating conditions, a rigorous understanding of theerosion physics was needed.

From the observed erosion trends in the BPT-4000, it was recognized thatto fully understand such physics one must account, at minimum, for the2-D distribution of the electric field near the eroding surfaces, thesheath physics, and the local topology of the magnetic field. To accountfor all these physics, it is required usually that the solution to anextensive system of governing laws for the Hall thruster plasma isobtained, in two or three dimensions. The importance of understandingthe erosion physics in such topologies motivated the development of aHall thruster plasma solver named “Hall2De.”

Hall2De is a 2-D computational solver of the laws that govern theevolution of the partially-ionized gas in Hall thrusters. The code is adescendant of OrCa2D, a 2-D computational model of electric propulsionhollow cathodes that employs a mix of implicit and explicit algorithmsto solve numerically the plasma conservation laws in these devices. InHall2De, excessive numerical diffusion due to the large disparity of thetransport coefficients parallel and perpendicular to the magnetic fieldis evaded by discretizing the equations on a computational mesh that isaligned with the applied magnetic field. This magneticfield-aligned-mesh (MFAM) capability was largely motivated by the needto assess the life of Hall thrusters in complicated magnetic fieldtopologies. A detailed description of the code has been provided byMikellides, et al. (I. G. Mikellides, I. Katz, R. R. Hofer, and D. M.Goebel, Proceedings of the 31st International Electric PropulsionConference, Ann Arbor, Mich. (Electric Rocket Propulsion Society,Fairview Park, Ohio., 2009), IEPC Paper No. 09-114).

There is a need for improved electric propulsion devices with greaterthroughput capabilities for many space applications.

SUMMARY OF THE INVENTION

According to one aspect, the invention features a Hall thruster having aconductive wall. The Hall thruster comprises an annular dischargechamber having a conductive wall and having a rear surface with anaperture defined therein, the conductive wall of the annular dischargechamber having a selected one of a wall shape, a profile and a crosssection fabricated in accordance with a respective calculated wallshape, calculated profile, and calculated cross section deduced to besubstantially a respective one of a wall shape, a profile and a crosssection that would be present in the Hall thruster at an end of lifeoperating state; an anode/gas distributor having an anode electricalterminal, the anode/gas distributor situated in the aperture defined inthe rear surface of the annular discharge chamber, the anode/gasdistributor having at least one inlet configured to receive an ionizablegas and configured to distribute the ionizable gas for use as apropellant; a cathode neutralizer configured to provide electrons, thecathode neutralizer having a cathode electrical terminal that can beconnected to the anode electrical terminal by way of a power supply anda switch, the cathode neutralizer and the anode/gas distributor whenoperating generating an axial electrical field within the annulardischarge chamber; and a magnetic circuit having a magnetic yoke, aninner magnetic coil and an outer magnetic coil, the magnetic circuitconfigured to be switchably powered by a power supply, the magneticcircuit configured to provide a substantially radial magnetic fieldacross the annular aperture of the annular discharge chamber, themagnetic circuit configured to provide a magnetic field that providesmagnetic shielding of the conductive wall of the annular dischargechamber from charged particles.

In one embodiment, the conductive wall comprises graphite.

In another embodiment, the conductive wall comprises a metal.

In yet another embodiment, the conductive wall comprises a form ofcarbon other than graphite.

In still another embodiment, the end of life operating state is a statethat exists after at least 10,000 hours of operation.

In a further embodiment, the calculated wall shape, the calculatedprofile, and the calculated cross section is a respective calculatedwall shape, calculated profile, and calculated cross section deducedusing a code employing a magnetic field-aligned-mesh.

In still a further embodiment, the code employing a magneticfield-aligned-mesh comprises a Hall2De code.

In yet a further embodiment, the ionizable gas is a gas selected fromthe group of gases consisting of xenon, krypton and argon.

In still another embodiment, the ionizable gas comprises a vaporproduced from an element selected from the group of elements consistingof bismuth, iodine, magnesium and zinc.

In an additional embodiment, the conductive wall is configured toprovide higher emissivity than a wall having a respective one of thesame wall shape, the same profile and the same cross section constructedfrom a non-conductor.

In one more embodiment, the conductive wall is configured to provide awall of higher strength than a respective one of the same wall shape,the same profile and the same cross section constructed from anon-conductor.

In yet another embodiment, the rear surface of the annular dischargechamber is fabricated from graphite.

The foregoing and other objects, aspects, features, and advantages ofthe invention will become more apparent from the following descriptionand from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The objects and features of the invention can be better understood withreference to the drawings described below, and the claims. The drawingsare not necessarily to scale, emphasis instead generally being placedupon illustrating the principles of the invention. In the drawings, likenumerals are used to indicate like parts throughout the various views.

FIG. 1A is an image of a conventional Hall thruster.

FIG. 1B is an image of a Hall thruster in the magnetically shieldedconfiguration.

FIG. 1C is an image of a Hall thruster in the magnetically shieldedconfiguration constructed entirely with graphite walls.

FIG. 2A is a graph of total efficiency for a conventional (baseline)Hall thruster built with BN components (triangle), a magneticallyshielded Hall thruster built with BN (squares), and a magneticallyshielded Hall thruster built with graphite walls (diamonds) versus innercoil current.

FIG. 2B is a graph of discharge current for a conventional (baseline)Hall thruster built with BN components (triangle), a magneticallyshielded Hall thruster built with BN (squares), and a magneticallyshielded Hall thruster built with graphite walls (diamonds) versus innercoil current.

FIG. 2C is a graph of thrust for a conventional (baseline) Hall thrusterbuilt with BN components (triangle), a magnetically shielded Hallthruster built with BN (squares), and a magnetically shielded Hallthruster built with graphite walls (diamonds) versus inner coil current.

FIG. 2D is a graph of total Isp for a conventional (baseline) Hallthruster built with BN components (triangle), a magnetically shieldedHall thruster built with BN (squares), and a magnetically shielded Hallthruster built with graphite walls (diamonds) versus inner coil current.

FIG. 3 is a graph of wall temperature a conventional (baseline) Hallthruster built with BN components (squares), a magnetically shieldedHall thruster built with BN (Triangles), and a magnetically shieldedHall thruster built with graphite walls (diamonds) versus total power.

FIG. 4A is a schematic cross sectional diagram of a prior art Hallthruster design.

FIG. 4B is a schematic cross sectional diagram of a prior art Hallthruster design, showing the magnetic field lines present in anoperating device.

FIG. 5 is an image of a prior art Hall thruster in operation.

FIG. 6 is a schematic cross sectional diagram of a magnetically shieldedHall thruster design according to principles of the invention.

FIG. 7 is an image of a magnetically shielded Hall thruster inoperation, showing the minimal interaction of the magnetic field lineswith the wall.

FIG. 8 is a close-up image of a magnetically shielded Hall thruster inoperation, showing that the magnetic shielding holds the plasma off thewall, providing an unrestricted view along the wall to the anode.

FIG. 9 is a graph of the operating parameters of the baselineconfiguration with high electron temperature (squares) and largepotential drop (diamonds) along the wall surface.

FIG. 10 is a graph of the operating parameters of themagnetically-shielded configuration with low electron temperature(squares) and constant potential (diamonds) along the wall surface.

FIG. 11A is an image of an inner insulator ring from the baselineconfiguration, showing an eroded white region (about 4 mm erosion band)at the edge of the ring.

FIG. 11B is an image of an inner insulator ring from themagnetically-shielded configuration showing a deposited black graphiteconducting layer on the surface in contact with the plasma. The thrusterperformance was unaffected by the conducting rings, indicating thatconducting walls, such as metallic walls or graphite walls, could beused.

FIG. 12A is a high-level flow chart showing the relationships among theinput parameters, the Hall2De code and the output results.

FIG. 12B is a flow chart showing the main components of the Hall2Decode.

FIG. 13 is a diagram that illustrates the nomenclature used inperforming Hall2De computations for a prior art thruster.

DETAILED DESCRIPTION

We have demonstrated by reduction to practice the feasibility of a newconcept intended to significantly reduce the cost and mass of Hallthrusters by replacing the dielectric discharge chamber walls normallyused in Hall thrusters with simple, inexpensive, conductive materialssuch as graphite. This is enabled by the large reduction in theplasma-wall interactions discovered with a unique magnetic fieldconfiguration in the thruster called magnetic shielding. Magneticshielding has been described in detail in co-pending U.S. provisionalpatent application Ser. No. 61/599,174, filed Feb. 15, 2012, and incopending U.S. provisional patent application Ser. No. 61/745,041, filedDec. 21, 2012. It is believed that other conductive materials, such asstainless steel, or other metals, can also be used as the material ofconstruction of the chamber walls.

Hall thrusters with magnetic shielding don't require the insulatingfeatures of ceramic (typically boron nitride) walls, and therefore canbe fabricated and operated with electrically conducting walls withoutsignificantly impacting the thruster performance. This makes it simplerand less expensive to fabricate a thruster to survive launch loads. Inaddition, the graphite discharge chamber radiates more efficiently whichincreases the power capability of the thruster compared to conventionalHall thruster designs.

The magnetically shielded (MS) H6 Hall thruster design was retrofittedwith new walls fabricated of graphite and then tested to compare theperformance to previous thruster data obtained with standard BoronNitride (BN) walls. The H6 Hall thruster is designed with replaceable“rings” near the thruster exit plane where the plasma contacts the wallsto provide the ability to measure the erosion rate by removing the ringsand measuring the surface on a precision coordinate measuring machine(CMM). Using a CMM, small rings of conducting-materials can be easilyand quickly fabricated and tested. In a preferred embodiment, graphiteis used as the material for the rings is because it features a very highemissivity to efficiently radiate any deposited power, and it has goodstrength and a reduced mass as compared to stainless steel.Nevertheless, in other embodiments, one might wish to use a conductorother than graphite as the material of construction, such as carbon insome other form, or another conductive material, such as a metal.

The H6 Hall thruster was tested with graphite walls at the nominaldesign (6 kW) power level for which this thruster was designed. Asdescribed hereinbelow, the graphite wall magnetically shielded H6 Hallthruster demonstrated performance nearly identical (within 2%) to thedesign with boron nitride walls, which successfully demonstrates thefeasibility of this embodiment. This is a remarkable result becauseprevious work in the US and France with graphite walls in Hall thrusterswithout magnetic shielding resulted in a reduction in the thrusterefficiency and performance (thrust and Isp) by factors of about 2compared to ceramic walls due to shorting out of the electric fields atthe walls by the conductor. This performance degradation was avoided inthe present invention because of the characteristics of magneticshielding that largely isolates the main thruster plasma discharge fromthe thruster walls.

The three configurations of the H6 Hall thruster used for comparison areshown in FIG. 1A, FIG. 1B and FIG. 1C.

FIG. 1A is an image of a conventional Hall thruster, having an annulardischarge chamber 102 with a non-conductive outer wall 104 and anon-conductive inner wall 106.

FIG. 1B is an image of a Hall thruster in the magnetically shieldedconfiguration, having an annular discharge chamber 112 with anon-conductive outer wall 114 and a non-conductive inner wall 116. Themagnetic shielding apparatus is powered by way of wires 130.

FIG. 1C is an image of a Hall thruster in the magnetically shieldedconfiguration constructed entirely with graphite walls, having anannular discharge chamber 122 made of graphite, a graphitenon-conductive outer wall 124 and a graphite non-conductive inner wall126. The magnetic shielding apparatus is powered by way of wires 140.

Performance Data

Critical thruster performance data (total efficiency, discharge current,thrust, and Isp) were obtained for all three configurations shown inFIG. 1A, FIG. 1B, and FIG. 1C.

FIG. 2A is a graph of total efficiency for a conventional (baseline)Hall thruster built with BN components (triangle), a magneticallyshielded Hall thruster built with BN (squares), and a magneticallyshielded Hall thruster built with graphite walls (diamonds) versus innercoil current.

FIG. 2B is a graph of discharge current for a conventional (baseline)Hall thruster built with BN components (triangle), a magneticallyshielded Hall thruster built with BN (squares), and a magneticallyshielded Hall thruster built with graphite walls (diamonds) versus innercoil current.

FIG. 2C is a graph of thrust for a conventional (baseline) Hall thrusterbuilt with BN components (triangle), a magnetically shielded Hallthruster built with BN (squares), and a magnetically shielded Hallthruster built with graphite walls (diamonds) versus inner coil current.

FIG. 2D is a graph of total Isp for a conventional (baseline) Hallthruster built with BN components (triangle), a magnetically shieldedHall thruster built with BN (squares), and a magnetically shielded Hallthruster built with graphite walls (diamonds) versus inner coil current.

Plotting the performance results versus this coil current parameterillustrates the variation in performance with magnetic field strengthnear the exit plane, which is a design parameter in Hall thrusters. Themagnetically shielded (MS) thruster has nearly the same efficiency(within 2%) as the baseline unshielded design, but the thrust is reducedand the Isp increased relative to the baseline performance. The thrustdecrease was found to be due to plume divergence angle increases in themagnetically shielded configuration due to the field shape and movementof the plasma downstream by a few millimeters. The Isp increase wasfound to be due to a larger amount of higher ionized ions in the plume,which increase the ion velocity and therefore the Isp.

In the magnetically shielded Hall thruster, the rings/walls are near theanode potential, and not the cathode potential. The magnetic field isnear zero at the anode. The channel depth is still longer than channelwidth. The acceleration zone is near the exit plane. This indicates thatthe magnetically shielded Hall thruster does not use an anode layeracceleration mechanism, and therefore it is not a thruster with anodelayer (TAL).

This innovation could lead to higher power densities, because thethruster power level likely now limited by anode dissipation(radiation). Therefore, the entire channel can be made of one or morepieces of material at anode potential, thereby providing a largeradiator. Graphite is such a material.

Replacement of the boron nitride rings with graphite reduced theefficiency by another 1 to 2%, with similar reductions in thrust. Theslight difference between the graphite wall and the boron nitride is notconsidered significant.

Other Results

A significant observation of the benefit of magnetic shielding andconductive wall made of graphite is the change in the thruster walltemperature in the three configurations. The wall temperature wasmeasured during operation by a FLIR Inframetrics PM 380 Infrared ImagingSystem camera that was calibrated by observations of heated boronnitride and graphite samples placed in the test facility next to thethruster, and by thermocouples embedded into the rings. The temperatureof the outer ring measured by the thermal camera as a function of totalpower into the H6 thruster for the three configurations is shown in FIG.3. The inner ring temperature was found to be essentially the same asthe outer ring. In the baseline unshielded case with boron nitridewalls, the temperature of the outer ring increases from 291° C. at 1.5kW to about 520° C. at 6 kW. The introduction of magnetic shieldingreduces the boron nitride ring temperature at 6 kW to about 465° C. Thereduction in the wall temperature with magnetic shielding is believed tobe a result of reduced plasma bombardment of the wall. Installation ofthe graphite rings further reduced the wall temperature at 6 kW by anadditional 50° C. to 415° C. This reduction is primarily attributed tothe increased emissivity of graphite compared to boron nitride, whichradiates the deposited power in the ring more efficiently.

Using the surface temperature measured by the camera, the emissivity ofthe material, and the surface geometry of the insert rings, wall, andanode, the radiated power for each of the rings in the threeconfigurations can be calculated and is shown in Table 1.

TABLE 1 Component BL BN MS BN MS C Anode  91 W 119 W 111 W Inner Ring297 W 147 W 119 W Outer Ring 310 W 140 W 110 W Inner Wall  98 W  95 W 98 W Outer Wall 229 W 247 W 258 W Total Power 1025 W  748 W 696 W

By adding these values together, the total power radiated by the ringsis calculated to be roughly 1025 W, 748 W, and 696 W for the H6 baselineBoron Nitride (H6BL-BN), H6 magnetically shielded Boron Nitride(H6MS-BN), and H6 magnetically shielded graphite (H6MS-graphite)configurations respectively at 6 kW of total input power. Thus,replacing the BN insert rings with graphite rings causes a reduction inpower losses due to thermal radiation by roughly 32% and reduces theradiated power from the rings by more than a factor of 2 compared to theH6BL-BN configuration. Therefore the lower temperature of the graphiterings results from both a higher emissivity and a slightly lower powerdeposition from the plasma. It is posited that the temperature of thewalls could be decreased further if the BN discharge chamber walls werealso replaced with graphite in the H6MS configuration such that thetotal radiation area for deposition of power in the anode region isincreased. Given this decrease in radiated power as well as the decreasein ring, wall, and anode temperatures at higher operating powers, itfollows that the use of magnetic shielding techniques and graphitedischarge chambers will likely result in a higher power densitycapability for future Hall thrusters of this design.

It is believed that this work represents a major advancement in HallThruster technology by the shielding of the walls from ion bombardmentand erosion with specially shaped magnetic fields and then replacing thetraditional ceramic walls with graphite. This advance greatly simplifiesconstruction of the thruster required to withstand launch vibrations byeliminating large fragile ceramics and ceramic support structures, andwill thereby lead to significant reductions in the thruster mass andcost. The new design could also lead to factors of two to three increasein the thruster power density, resulting in ultra-compact, very longlife Hall thrusters for space missions. Finally, the magnetic shieldingtechnology eliminates wall erosion at higher voltages, which alsoenables long life operation at higher Isp.

In a preferred embodiment, the profile of the wall of the thruster canbe modeled using the Hall2De code. It is expected that it will beadvantageous to provide initial Hall wall profiles that conform to thecalculated “end-of-life” wall profiles that computations using theHall2De code indicate will be produced if erosion were to be allowed tooccur, so that the operation of the Hall thruster for its initialoperation will be substantially invariant with time of operation frominitial operation until the supply of gas available to the thruster isexhausted.

The significant advantages of this thruster design in long life, lowcost and mass, and higher power density will also likely result in itreplacing convention Hall thrusters for both deep space prime propulsionapplications and commercial communications satellite station keepingapplications.

Having described the demonstrated results of the metallic (orconductive) wall Hall thruster that has been constructed and operatedsuccessfully, we will now describe some of the underlying Hall thrustertechnology, for those who may not be expert in this field.

FIG. 4A is a schematic cross sectional diagram of a prior art Hallthruster design. The conventional Hall thruster operates in a reducedpressure environment, such as space in which charged particles can begenerated by bombarding atoms with electrons. A Hall thruster typicallyuses a gas that can be ionized, such as Xenon, as the material that isaccelerated by the thruster, which results in an equal and oppositeacceleration experienced by the thruster (and the object to which it isattached). Xenon gas is used because of its high atomic weight and lowionization potential. Other materials that can be used as propellantsinclude krypton, argon, iodine, bismuth, magnesium and zinc.

As illustrated in FIG. 4A, an annular discharge chamber 408 whichtypically is constructed with non-conductive walls 404, such as BNmaterial, is provided with an anode/gas distributor 402 through whichthe gas is introduced into the thruster. The anode/gas distributor 402is conductive and has an electrical terminal. A cathode neutralizer 406that has an electrical terminal is provided, so that a voltage appliedby a switchable power supply connected between the anode electricalterminal and the cathode electrical terminal can generate free electronsthat are accelerated by an axial electric field 420. A magnetic circuit410, such as a yoke made of a magnetic material, connects an innermagnetic coil 412 and an outer magnetic coil 414 so as to provide aradial magnetic field 422.

The electrons are constrained to move in a closed path by the relationE×B so that they are trapped in the vicinity of the exit plane of thethruster above the anode/gas distributor 402 and have a high probabilityof ionizing a gas atom. Since E (the electric vector 420) points axiallyand B (the magnetic vector 422) points radially (e.g., from the centralpost of the magnetic yoke that passes through the inner magnetic coil412 to the portions of the magnetic yoke adjacent the outer magneticcoil 414, which would be radially outward, or in the opposite direction,which is radially inward), the vectorial cross product E×B results in alocal resultant that is oriented in a tangential direction relative tothe annular opening of the annular discharge chamber 408, which iseither clockwise or counterclockwise as viewed along a central axis ofthe Hall thruster depending on the direction of B. Therefore, theelectrons travel in circular path above the anode/gas distributor 402.Because the ionized gas atoms have much larger mass than the electronmass, they are not trapped by the magnetic field but are accelerated bythe electric field, producing thrust as an exhaust plume 430. The gasions pull an equal number of electrons with them, creating a plume withno net charge.

FIG. 4B is a schematic cross sectional diagram of a prior art Hallthruster design, showing the magnetic field lines present in anoperating device that does not include magnetic shielding.

FIG. 5 is an image of a prior art Hall thruster such as that of FIG. 4Aor FIG. 4B in operation.

FIG. 6 is a schematic cross sectional diagram of a magnetically shieldedHall thruster design according to principles of the invention. The wallshape, profile, or cross section is fabricated in accordance with acalculated wall shape, a calculated profile, or a calculated crosssection deduced using a code employing a magnetic field-aligned-mesh (MFAM) such as Hall2De.

FIG. 7 is an image of a magnetically shielded Hall thruster inoperation, showing the minimal interaction of the magnetic field lineswith the wall.

FIG. 8 is a close-up image of a magnetically shielded Hall thruster inoperation, showing that the magnetic shielding holds the plasma off thewall, providing an unrestricted view along the wall to the anode, as isindicated by the arrow.

FIG. 9 is a graph of the operating parameters of the baselineconfiguration with high electron temperature (squares) and largepotential drop (diamonds) along the wall surface.

FIG. 10 is a graph of the operating parameters of themagnetically-shielded configuration with low electron temperature(squares) and constant potential (diamonds) along the wall surface.

FIG. 11A is an image of an inner insulator ring from the baselineconfiguration, showing an eroded white region (about 4 mm erosion band)at the edge of the ring.

FIG. 11B is an image of an inner insulator ring from themagnetically-shielded configuration showing a deposited black graphiteconducting layer on the surface in contact with the plasma. The thrusterperformance was unaffected by the conducting rings, indicating thatconducting walls, such as metallic walls or graphite walls, could beused.

Computation Methods

FIG. 12A is a high-level flow chart showing the relationships among theinput parameters, the Hall2De code and the output results. FIG. 12B is aflow chart showing the main components of the Hall2De code. A moredetailed discussion of the theory underlying the computation has beenpresented in co-pending U.S. provisional patent application Ser. No.61/599,174, filed Feb. 15, 2012, and in co-pending U.S. provisionalpatent application Ser. No. 61/745,041, filed Dec. 21, 2012, which havebeen incorporated by reference, and which will become part of the publicrecord when this application publishes and/or issues as a patent. Giventhe voluminous description presented there, a brief summary will bepresented here and the reader is directed to review the two provisionalapplication documents.

As shown in FIG. 12A, the computation includes inputs for thrustergeometry, the magnetic field, and thruster operational, physical andnumerical specifications. Using the thruster geometry and the magneticfield, a magnetic field aligned mesh (MFAM) generator provides aspecific coordinate system for the calculation. Using the specificcoordinate system, boundary conditions are applied, and the physicaldomain of the thruster being modeled is generated.

The major distinctive features of Hall2De are: (1) discretization of allconservation laws on a MFAM, (2) numerical solution of the heavy-speciesconservation equations without invoking discrete-particle methods, sothat multiple ion fluids can be included each being treated as anisothermal, cold (relative to the electrons) fluid accounting for thedrag force and ion pressure gradient, the evolution of the(collisionless) neutral species is computed using line-of-sightformulations that account for ionization, and (3) a large computationaldomain that extends several times the thruster channel length in theaxial direction and encompasses the cathode boundary and the axis ofsymmetry.

Discretization of all the conservation laws allows for the assessment oferosion in regions with complex magnetic field topologies. In regions ofthe thruster where isothermalization and thermalizedequipotentialization of the lines of force persists, computationalelement would be subdivided into additional elements using an orthogonalset of lines. The equations are then solved on each one of theseadditional elements. The main advantage here is the ability to simulateregions of the thruster where surfaces have disrupted the lines offorce. The MFAM also allows for the self-consistent simulation of theplasma in the near-anode region. No magnetic field streamline in thisregion of Hall2De need be identified upstream of which the conservationlaws for the plasma are not solved self-consistently. Numerical solutionof the heavy-species conservation equations without invokingdiscrete-particle methods eliminates the inherent statisticalfluctuations typically caused by particle-based methods. A largecomputational domain allows for the investigation of the large-scalebehavior of electrons in the plume while accounting for the cathodeboundary conditions self-consistently.

The output from the Hall2De ionized gas solver include numericaldiagnostics, temporal results for the thruster performance and for theelectrical circuit, and spatial results for the ionized gas flow andthruster erosion. This last result allows one to determine geometriesfor components such as the anode walls that are expected to be “steadystate” after long operation, and can allow modeling using the “steadystate” geometries as input geometries to see if they will be essentiallyinvariant with time of operation.

As shown in FIG. 12B, the Hall2De ionized gas solver reads an input filethat describes what is to be computed, and determines whether it isdoing a cold start or not. For a cold start, the variables for geometryand physics are initialized. If there is not a cold start, a restartfile is read in, which allows the computation to pick up after apredetermined number of cycles have previously been performed. Aniteration counter is set to 1 and increments at the end of eachiteration. A computation cycle is performed in which plasma and neutralgas conservation equations are utilized. At the end of the cycle, acheck for the number of iterations that have been performed is one, andif the number is less than a predetermined number, another calculationcycle is performed. When the predetermined number of iterations has beencarried out, the output is written and a restart file is written. Thecalculation can then end. The computations are performed on one or moregeneral purpose programmable computers running under the control ofinstructions recorded on a machine readable medium.

FIG. 13 is a diagram that illustrates the nomenclature used inperforming Hall2De computations for a prior art thruster. In thediagram, a comparison to previous calculation methods, known as theHPHall method, is given. In FIG. 13, the walls adjacent the anode/gasdistributor are indicated as being dielectric (non-conductive) walls. Ashas been described, computations for Hall thrusters having conductivewall (or metallic walls) have also been performed.

Theoretical Discussion

Although the theoretical description given herein is thought to becorrect, the operation of the devices described and claimed herein doesnot depend upon the accuracy or validity of the theoretical description.That is, later theoretical developments that may explain the observedresults on a basis different from the theory presented herein will notdetract from the inventions described herein.

Any patent, patent application, patent application publication, journalarticle, book, published paper, or other publicly available materialidentified in the specification is hereby incorporated by referenceherein in its entirety. Any material, or portion thereof, that is saidto be incorporated by reference herein, but which conflicts withexisting definitions, statements, or other disclosure materialexplicitly set forth herein is only incorporated to the extent that noconflict arises between that incorporated material and the presentdisclosure material. In the event of a conflict, the conflict is to beresolved in favor of the present disclosure as the preferred disclosure.

While the present invention has been particularly shown and describedwith reference to the preferred mode as illustrated in the drawing, itwill be understood by one skilled in the art that various changes indetail may be affected therein without departing from the spirit andscope of the invention as defined by the claims.

The invention claimed is:
 1. A Hall thruster, comprising: an annulardischarge chamber having an inner wall, the entire inner wall being madeof an electrically conductive material and having a rear surface with anaperture in the inner wall defined therein, said inner wall of saidannular discharge chamber having a downstream end, a radially innersurface, and a radially outer surface, wherein said radially innersurface and said radially outer surface respectively radially inwardlyand radially outwardly bound said annular discharge Chamber, and whereinsaid radially inner surface diverges radially inwardly at saiddownstream end and wherein said radially outer surface diverges radiallyoutward at said downstream end; an anode/gas distributor configured todistribute a gas and situated in said aperture defined in said rearsurface of said annular discharge chamber; a cathode neutralizer; and amagnetic circuit having a magnetic yoke, an inner magnetic coil and anouter magnetic coil, said magnetic circuit configured to be switchablypowered, said magnetic circuit configured to provide a substantiallyradial magnetic field across an annular aperture of said annulardischarge chamber, said magnetic circuit configured to provide magneticshielding of said inner wall of said annular discharge chamber fromcharged particles, wherein the inner wall is configured to float at asame electrical potential of the anode/gas distributor.
 2. The Hallthruster of claim 1, wherein said inner wall comprises graphite.
 3. TheHall thruster of claim 1, wherein said inner wall comprises a metal. 4.The Hall thruster of claim 1, wherein said inner wall comprises a formof carbon other than graphite.
 5. The Hall thruster of claim 1, whereinerosion of the inner wall is prevented for 10,000 hours of operation. 6.The Hall thruster of claim 1, wherein said gas is selected from thegroup of gases consisting of xenon, krypton and argon.
 7. The Hallthruster of claim 1, wherein said gas comprises a vapor produced from anelement selected from the group of elements consisting of bismuth,iodine, magnesium and zinc.
 8. The Hall thruster of claim 1, whereinsaid inner wall has a wall shape, a profile, and a cross section, andwherein said inner wall is configured to provide higher emissivity thana non-electrically conductive inner wall having the same shape, profileand cross section.
 9. The Hall thruster of claim 1, wherein said innerwall has a wall shape, a profile, and a cross section, and wherein saidinner wall is configured to be of higher strength than anon-electrically conductive inner wall having the same shape, profileand cross section.
 10. The Hall thruster of claim 1, wherein said rearsurface is fabricated from graphite.